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Vahid. K. Alilou & Mohammad. Teshnehlab.

International Journal of Engineering (IJE), Volume (3) : Issue (6) 565

Prediction of 28-day compressive strength of concrete on thethird day using artificial neural networks

Vahid. K. Alilou [email protected] of Computer EngineeringScience and Research Branch, IslamicAzad University, Tehran, IranKhvoy, 58197-38131, IRAN

Mohammad. Teshnehlab [email protected] of Electronic EngineeringK.N. Toosi University of Technology, Tehran, IranTehran, IRAN

Abstract

In recent decades, artificial neural networks are known as intelligent methods formodeling of behavior of physical phenomena. In this paper, implementation of anartificial neural network has been developed for prediction of compressivestrength of concrete. A MISO (Multi Input Single Output) adaptive system hasbeen introduced which can model the proposed phenomenon. The data hasbeen collected by experimenting on concrete samples and then the neuralnetwork has been trained using these data. From among 432 specimens, 300data sample has been used for train, 66 data sample for validation and 66 datasample for the final test of the network. The 3-day strength parameter of concretein the introduced structure also has been used as an important index forpredicting the 28-day strength of the concrete. The simulations in this paper are

based on real data obtained from concrete samples which indicate the validity ofthe proposed tool.

Keywords:Concrete, Strength, Prediction, Artificial, Neural Networks.

1. INTRODUCTION

Different sciences are developing fast in today's world. In recent decades, man has seenincreased relationship of sciences in different fields and the more relationship has led to theappearance of the more new knowledge and technology. Nowadays, one of the most importantproblems of man are technical and engineering problems. The complexity of the most of the

problems in this field has made the experts of this field use the new mathematical and modelingmethods for solving this type of problems. Intelligent systems can be used as suitable tools foridentifying complex systems, due to their ability of learning and adaptation.One of the complex problems in our world is the problem of the concrete. The main criterion forevaluating the compressive strength of concrete is the strength of the concrete on 28

thday. The

concrete sample is tested after 28 days and the result of this test is considered as a criterion forquality and rigidity of that concrete.

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Concrete is the most widely used structural material in constructions in the world. Massiveconcreting in huge civil projects like dams, power plants, bridges and etc usually is notpracticable and it is necessary to be performed in several layers and the compressive strength ofeach layer should not be less than the specified compressive strength. Therefore one should wait28 days to achieve 28-day strength of each layer of concrete. Thereupon if we have n layers ofconcrete we need 28ndays to complete the total project. [1]

2. CONCRETE

Concrete is the only major building material that can be delivered to the job site in a plastic state.This unique quality makes concrete desirable as a building material because it can be molded tovirtually any form or shape. Concrete provides a wide latitude in surface textures and colors andcan be used to construct a wide variety of structures, such as highways and streets, bridges,dams, large buildings, airport runways, irrigation structures, breakwaters, piers and docks,sidewalks, silos and farm buildings, homes, and even barges and ships.The two major components of concrete are a cement paste and inert materials. The cement pasteconsists of Portland cement, water, and some air either in the form of naturally entrapped airvoids or minute, intentionally entrained air bubbles. The inert materials are usually composed offine aggregate, which is a material such as sand, and coarse aggregate, which is a material such

as gravel, crushed stone, or slag.When Portland cement is mixed with water, the compounds of the cement react to form acementing medium. In properly mixed concrete, each particle of sand and coarse aggregate iscompletely surrounded and coated by this paste, and all spaces between the particles are filledwith it. As the cement paste sets and hardens, it binds the aggregates into a solid mass.Under normal conditions, concrete grows stronger as it grows older. The chemical reactionsbetween cement and water that cause the paste to harden and bind the aggregates togetherrequire time. The reactions take place very rapidly at first and then more slowly over a long periodof time. [2]

3. CEMENT

Cement is a material that has adhesive and cohesive properties enabling it to bond mineral

fragments into a solid mass. Cement consists of silicates and aluminates of lime made fromlimestone and clay (or shale) which is ground, blended, fused in a kiln and crushed to a powder.Cement chemically combines with water (hydration) to form a hardened mass. The usualhydraulic cement is known as Portland cement because of its resemblance when hardened toPortland stone found near Dorset, England. The name was originated in a patent obtained byJoseph Aspdin of Leeds, England in 1824.Typical Portland cements are mixtures of tricalcium silicate (3CaO SiO2), tricalcium aluminate(3CaO Al2O3), and dicalcium silicate (2CaO SiO2), in varying proportions, together with smallamounts of magnesium and iron compounds. Gypsum is often added to slow the hardeningprocess. [2,3]

4. WATER

The water has two roles in concrete mixture: First is the chemical composition with cement and

perform cement hydration and second is to make the concrete composition fluent and workable.The water which is used to make the concrete is drink water. The impurity of water can haveundesirable effect on concrete strength. [4]

5. AGGREGATES

Since aggregate usually occupies about 75% of the total volume of concrete, its properties have adefinite influence on behavior of hardened concrete. Not only does the strength of the aggregateaffect the strength of the concrete, its properties also greatly affect durability (resistance todeterioration under freeze-thaw cycles). Since aggregate is less expensive than cement it is

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logical to try to use the largest percentage feasible. Hence aggregates are usually graded by sizeand a proper mix has specified percentages of both fine and coarse aggregates. Fine aggregate(sand) is any material passing through a No. 4 sieve. Coarse aggregate (gravel) is any material oflarger size.Fine aggregate provides the fineness and cohesion of concrete. It is important that fine aggregateshould not contain clay or any chemical pollution. Also, fine aggregate has the role of space fillingbetween coarse aggregates. Coarse aggregate includes: fine gravel, gravel and coarse gravelIn fact coarse aggregate comprises the strongest part of the concrete. It also has reverse effecton the concrete fineness. The more coarse aggregate, the higher is the density and the lower isthe fineness. [3,5]

6. COMPRESSIVE STRENGTH OF CONCRETE

The strength of concrete is controlled by the proportioning of cement, coarse and fine aggregates,water, and various admixtures. The ratio of the water to cement is the chief factor for determiningconcrete strength as shown in figure1. The lower the water-cement ratio, the higher is thecompressive strength. A certain minimum amount of water is necessary for the proper chemicalaction in the hardening of concrete; extra water increases the workability (how easily the concretewill flow) but reduces strength. A measure of the workability is obtained by a slump test.Actual strength of concrete in place in the structure is also greatly affected by quality control

procedures for placement and inspection. The strength of concrete is denoted in the UnitedStates by f'c which is the compressive strength of test cylinder 6 in. in diameter by 12 in. highmeasured on the 28th day after they are made. [3]

42

49

0.4 0.5 0.6 0.70.3

7

14

21

28

35

56

Tensile Strength

CompressiveStrength

Strength(N/mm2

)

Water/Cement Ratio

FIGURE 1: illustration of the effect of water/cement ratio in concrete strength [1]

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7. CONCRETE SAMPLING

Acceptance of the concrete in the site is performed based on the results of the compressive testsof concrete samples. The concrete samples must be taken from the final consumption place.The purpose of the concrete sampling is to prepare two specimens of concrete which theircompressive tests will be performed after 28 days or in any predetermined day. To predict the 28-day compressive strength of concrete we can also have another sample to be tested earlier than

28 days. [1]

8. CONCRETE MIX DESIGN

The concrete mix design is a process of selecting the suitable ingredients of concrete anddetermining their most optimum proportion which would produce, as economically as possible,concrete that satisfies a certain compressive strength and desired workability. [6]The concrete mix design is based on the principles of

Workability

Desired strength and durability of hardened concrete

Conditions in site, which helps in deciding workability, strength and durabilityrequirements

9. ADAPTIVE SYSTEMS

Adaptability, in essence, is the ability to react in sympathy with disturbances to the environment.A system that exhibits adaptability is said to be adaptive. Biological systems are adaptivesystems; animals, for example, can adapt to changes in their environment through a learningprocess [7]. A generic adaptive system employed in engineering is shown in Figure 2. It consistsof

set of adjustable parameters (weights) within some filter structure;

An error calculation block (the difference between the desired response and the output ofthe filter structure);

A control (learning) algorithm for the adaptation of the weights.The type of learning represented in Figure 2 is so-called supervised learning, since the learning isdirected by the desired response of the system. Here, the goal is to adjust iteratively the free

parameters (weights) of the adaptive system so as to minimize a prescribed cost function in somepredetermined sense. [8]

- +

INPUTSIGNAL

CONTROLALGORITHM

OUTPUT DESIREDSIGNAL

ERROR

ADAPTIVE SYSTEM

STRUCTURE

FIGURE 2: Block diagram of an adaptive system

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10. ARTIFICIAL NEURAL NETWORKS

Artificial Neural Network (ANN) models have been extensively studied with the aim of achievinghuman-like performance, especially in the field of pattern recognition and system identification.These networks are composed of a number of nonlinear computational elements which operate inparallel and are arranged in a manner reminiscent of biological neural inter-connections.The property that is of primary significance for a neural network is the ability of the network to

learn from its environment, and to improve its performance through learning. The improvement inperformance takes place over time in accordance with some prescribed measure. A neuralnetwork learns about its environment through an interactive process of adjustments applied itssynaptic weights and bias levels. Ideally, the network becomes more knowledgeable about itsenvironment after each iteration of the learning process. [7]

11. CONCRETE STRENGTH PREDICTION

To predict 28-day strength of concrete, It should identify the effective parameters of the concretestrength. The more accurately identified the parameters, the better is the result.The studies in this paper were performed in two phases:

1. Phase one, includes the studies about the concrete and effective factors of the concretecompressive strength and also performing the experiments in the real environment andcollecting data.

2. Phase two, include studies about how to use artificial neural networks to identify thepresented system and to achieve accurate prediction of concrete 28-day compressivestrength. [1]

12. PERFORMING EXPERIMENTS

In this study the ACI method is used to perform experiments. Experiments were performed inAghchay dam in west Azerbaijan in IRAN. The cement used in the experiments was providedfrom Sofiyan cement plant and the aggregates were provided from the natural materials of theAghchay dam site. [1]

13. COLLECTING DATA

There are lots of Parameters affect on compressive strength of concrete. But the most important

parameters were collected in table 1. It is important that the range of each parameter is limiteddue to regarding ACI standard.

TABLE 1: Effective parameters of the compressive strength of the concrete

Row Parameter Unit Range

1 Mix Design - A-L

2 Water/Cement Ratio % 35.0 - 75.0

3 Density ton/m3 2.30 - 2.60

4 Slump mm 70 - 150

5 Air % 1.0 - 7.0

6 Silica fumes gr 0 - 4007 Super-Plasticizer kg 0.0 - 3.5

8 Age day 3, 7, 14, 28, 42

9 Compressive Strength kg/cm2 70.00 - 420.00

The concrete mix design is affected by these factors:Cement, Fine aggregate, Fine gravel, gravel, coarse gravel, air

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The 1st

to 7th

parameters are determined in the first day. There is a salient point about 8th

parameter (age). As previously mentioned, the concrete age has a direct arithmetic relation withthe concrete strength. The more aged the concrete the higher is the compressive strength. [1]Here is an interesting point so that the 3-day compressive strength of concrete has amathematical relation with the compressive strength of the same concrete in 7

th, 14

th, 28

thand

42th

day. Therefore it can be used as an important parameter for prediction of this system. Inother words, the 3-day compressive strength of concrete is a very good criterion to achieve the28-day compressive strength.It is conceived from figure.3 that the higher the 3-day compressive strength the higher is the 28-day compressive strength of the concrete. Figure.4 shows the relationship between 3-daycompressive strength and 28-day compressive strength for 4 types of concrete with variable w/cratios, this relation is linear relatively.

281 3 7 14

7.50

15.00

22.50

30.00

37.50

45.00

52.50

60.00

0.40

0.50

0.600.70

7.50

15.00

22.50

30.00

37.50

45.00

52.50

60.00

w/c

CompressiveStrength(N/mm2)

Concrete Age ( day ) FIGURE 3: illustration of relationship between age and compressive strength of concrete [1]

0

10

20

30

40

50

60

10 20 30 40

28-DayCompressiveStrength

3-Day Compressive Strength

FIGURE 4: illustration of relationship between 3-day and 28-day strength of concrete [1]

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14. METHODOLOGY OF CONCRETE STRENGTH NEURAL IDENTIFICATION

A methodology for concrete strength neural identification was developed. It is shownschematically in Figure 5. Three blocks can be distinguished in the scheme. Experimental results,forming a set of data on concrete, used for training and testing the neural network are an integralpart of block1.The experimental results as a set of patterns were saved in a computer file which was then used

as the input data for the network in block 2. The data were divided into data for training andtesting the neural network. The training patterns were randomly input into the network asfollowing:

1. 70% of total data for training of the neural network2. 15% of total data for validation of the neural network3. 15% of total data for testing of the neural network,

Set of Data

Neural NetworkInput Data

Training and testingof neural network

Output data

processing

Analysis of

obtained results

Block1

Block2

Block3

FIGURE 5: Block diagram of concrete compressive strength identification by means of neural networks [9]

If the neural network correctly mapped the training data and correctly identified the testing data, itwas considered trained. The obtained results were analyzed in block 3 whose output was

identified concrete compressive strength f'c. [9]

15. FEED-FORWARD NEURAL NETWORK

The Feed-forward neural network structure for prediction of concrete compressive strength isshown in Figure 6. Feed-forward networks often have one or more hidden layers of sigmoidneurons followed by an output layer of linear neurons. Multiple layers of neurons with nonlineartransfer function allow the network to learn nonlinear and linear relationships between inputs and

outputs. [10]The process of learning with teacher in this network is executed through a back-propagationalgorithm so that the network output converges to the desired output. The key distinguishingcharacteristic of this feed-forward neural network with the back-propagation learning algorithm isthat it forms a nonlinear mapping from a set of input stimuli to a set of output using featuresextracted from the input patterns. The network can be designed and trained to accomplish a widevariety of nonlinear mappings, some of which are very complex. This is because the neural unitsin the neural network learn to respond to features found in the input. [11]

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The number of input and output units is determined by dimensions of the data set whereas thenumber of hidden layer (M) is a free parameter which is adjusted to achieve the maximumperformance. Note that, M determines the degree of freedom of the system. Therefore we expectthat there was an optimum value for M. The criterion to achieve the optimum M is defined as:"The smallest M which causes minimum mse while the maximum error is small"

Fnet

1

1

Neuron 11

o 11

w11

Fnet

1

2

Neuron 12

o 21

w21

Fnet1

Neuron1

n

on1

w1

1

..

.

x o1

1

...

x2

x3

x

x0 1=

n1

n1

o01

1=

Fnet 21

Neuron 21

o12w1

2

Mix Design

Fineness

Air

Admixture

3-Day Strength

4

x1

x5

28-Day Strength

FIGURE 6: Diagram of the feed-forward neural network used for concrete compressive strength prediction

Figure.7 shows the mean squared error of the network output for validation and test data with 10iterations for each number of hidden neurons. Figure.8 shows the maximum error betweendesired outputs and the network outputs with 10 iterations for each number of hidden neurons.The optimum value in this structure is to choose M=11 for the number of hidden neurons.In order to backpropagage the error and update the network weights, Gradient-Descent, Quasi-Newton, Conjugate-Gradient and Levenberg-Marquardt Algorithms were used.

Gradient Descent kgkWkW =+ )()1(

Quasi Newton KK gHkWkW1

)()1(

=+

Conjugate Gradient

WgkWkW k +=+ +1)()1(

Where Wis the weight matrix, is the learning rate, gis the gradient of error and His the hessianmatrix of the cost function. [12]The levenberg-marquardt algorithm is like quasi-newton but it doesn't need to calculate hessianmatrix where it can be estimated as follows:

JJHT

= , eJE T= EIHkWkW +=+

.][)()1( 1

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0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 200

0.5

1

1.5

2

2.5

3

3.5

4

4.5

FIGURE 7: Diagram of mean squared error of the network output with 10 iterations for certain number of

neurons

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 200

1

2

3

4

5

6

7

8

9

10

FIGURE 8: Diagram of maximum error of the network output with 10 iterations for certain number of neurons

The results of above algorithms have been collected in Table 2. Each row of the table is the resultof average 40 iterations of each method. Evaluation criterion of adaptive systems was defined asfollowing formula:

%T

e

NAPEorcentageErrAveragePer

N

i i

i 100*1

:1

=

=

Where Ti is the desired output and ei is the output error. [13]

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TABLE 2: Comparison of different algorithms used for predicting the concrete compressive strength

Accuracy on data (%)Ave.TimeRow Algorithm

Train Validation Test Total (second)

1 Levenberg-Marquardt 99.436 99.389 99.397 99.407 7.7

2 Polak-Ribiere Conjugate Gradient 98.861 98.836 98.866 98.854 17.33 Fletcher-Powell Conjugate Gradient 98.713 98.675 98.695 98.694 12.4

4 Gradient Descent 98.584 98.567 98.606 98.586 24.3

5 Quasi-Newton 98.388 98.341 98.423 98.384 89.2

Maximum Error ( kg/cm2 ) epochs

1 Levenberg-Marquardt 5.830 5.056 4.437 5.108 58

2 Polak-Ribiere Conjugate Gradient 9.686 8.536 7.652 8.635 571

3 Fletcher-Powell Conjugate Gradient 10.758 9.457 8.597 9.604 368

4 Gradient Descent 11.897 10.376 9.018 10.430 1833

5 Quasi-Newton 13.825 11.539 10.691 12.018 1999

0 200 400 600 800 1000 1200

10

0

Best Validation Performance is 0.006671 at epoch 1131

MeanSquaredError(mse)

1231 Epochs

Train

Validation

Test

Best

FIGURE 9: Diagram of mean squared error in the feed-forward neural network

It is conceived from table 2, that the best structure for prediction of concrete strength is the firstmethod with levenberg-marquardt algorithm.Figure 9 shows the mse diagram of the cost function reduction for training, validation and testdata. The following results are being conceived from this figure.

1. The final mse is small and admissible2. The test dataset error and validation dataset error are almost equal.3. Over fitting was not happened

The diagram of figure.10 also shows the linear regression between network output and desiredoutput for training, validation, test and total data.

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200 250 300

180

200

220

240

260

280

300

320

340

Target

Output~=1*Target+4.3e-005

Training: R=1

Data

Fit

Y = T

200 250 300180

200

220

240

260

280

300

320

340

Target

Output~=1*Target+

-0.0

046

Validation: R=1

Data

Fit

Y = T

200 250 300

180

200

220

240

260

280

300

320

340

Target

Output~=1*Target+0.0

02

Test: R=1

Data

Fit

Y = T

200 250 300

180

200

220

240

260

280

300

320

340

Target

O

utput~=1*Target+0.0

0012

All: R=1

Data

Fit

Y = T

FIGURE 10: Diagram of the network output and desired output for train, validation, test and all data

16. CONCLUSION

In this paper, a practical approach has been presented for prediction of 28-day compressivestrength of concrete. Basically, in all of the methods have been resented previously, the 3-daycompressive strength of concrete was not considered as an important parameter.

From this point of view we can consider the proposed method as a new method in which the 3-day compressive strength parameter has been introduced as a very important index. [Ref: 13, 14,15, 16]The proposed technique can be used as a very useful tool for reducing the duration of the projectexecution in huge civil projects. For example, imagine if we have a massive concrete structurewhich requires 10 stages of concreting then we need at least 2810=280 days to complete thetotal project regarding to standards. Therefore this project will be finished after about 1 yearconsidering the frigid winter days which concreting is impossible.

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Using the proposed tool we can have a precise prediction of the 28-day compressive strength ofthe concrete on the third day. Thereupon we need 310=30 days to complete this project and this

is an important progress in order to reducing the duration of the civil projects execution.

17. REFERENCES

1. V. K. Alilou. Designing a learning machine for prediction of the compressive strength of theconcrete by using Artificial neural networks. M.sc Thesis, Science and Research Branch,Islamic Azad University,Tehran,Iran, August 2009

2. Microsoft Encarta Encyclopedia, Microsoft Corporation, (2009)3. Chu Kia Wang, Charles G. Salmon. Reinforced Concrete Design, Harper & Row Publishers,

USA, (1979)4. M. Teshnehlab, V. K. Alilou, Concrete strength prediction using learning machine and neural

networks. In 2nd

Joint Congress on Fuzzy and Intelligent Systems. Tehran, IRAN, 20085. J.D.Dewar. Computer Modeling of concrete mixture, E&FN Spon, LONDON, (1999)6. Rishi. Garge. Concrete Mix Design using Artificial Neural Network. M.sc Thesis, Thapar

Institute of Engineering and Technology, June 20037. Simon Haykin. Neural Networks A Comprehensive Foundation, Prentice-Hall, (1999)8. Danilo P. Mandic, Jonathon A. Chambers. Recurrent Neural Networks for Prediction, John

Willey & Sons Inc., (2001)9. Jerzy Hola, Krzysztof Schabowicz. Application of Artificial Neural Networks to determineconcrete compressive strength based on non-destructive tests. Journal of civil Engineeringand Management, 11(1):23-32, 2005

10. Howard Demuth, Mark Beale. Neural Network Toolbox, Mathworks, (1998)11. Madan M.Gupta, Liang Jin, Noriyasu Homma. Static and Dynamic Neural Networks, Wiley-

Interscience, (2003)12. Martin T. Hagan, Howard B. Demuth, Mark Beale. Neural Network Design, University of

Colorado Bookstore, (1996)13. Ilker Bekir Topcu, Mustafa Saridemir. Prediction of compressive strength of concrete

containing fly ash using Artificial Neural Networks and Fuzzy Logic. ScienceDirect,Computational Materials Science, 41(3):305-311, 2008

14. E. Rasa, H. Ketabchi, M. H. Afshar. Predicting Density and Compressive Strength ofConcrete Cement Paste Containing Silica Fume Using Artificial Neural Networks. ScientiaIranica, 16(1):32-42, 2009

15. Jong In Kim, Doo Kie Kim. Application of Neural Networks for Estimation of ConcreteStrength. KSCE Journal of Civil Engineering, 6(4):429-438, 2002

16. Ji Zong Wang, Xi-Juan Wang, Hong-Guang NI. An Algorithm of Neural Network andApplication to Data Processing in Concrete Engineering. Informatica Institute of Mathematicsand Informatics, 14(1):95-110, 2003

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